Boundary condition for the disturbing potential

First of all, we choose the parameters of the ellipsoid in such a way that the normal potential on its surface, Uq, is equal to the potential of the total field at points of the geoid, Wq. Then, Equation (2.294) is greatly simplified and we obtain 

the determination of heights of the quasi-geoid N requires knowledge of the disturbing potential T on the physical surface of the earth. As in the case of the Stokes problem, in order to calculate N we have to determine the disturbing potential, which obeys some boundary condition on the physical surface of the earth instead of the surface of a geoid. This is the main advantage of a new approach. 

---

Here g is the gravitational field on the physical surface of the earth, y the normal field on the surface S. At the same time, dT/dv and dy/dv have the same values along line V at both surfaces. This is the boundary condition for the disturbing potential and therefore we have to find the harmonic function regular at infinity and satisfying Equation (2.301) on the surface S. In this case, the physical surface of the earth is represented by S formed by normal heights, plotted from the reference ellipsoid. In other words, by leveling the position of the surface S becomes known. 

---